Provide an introduction to the BJT ampliifier. What are the relevant waveforms, and the working of the transistor as an amplifier?

A bipolar junction transistor (BJT) is a three-terminal electronic component constructed of doped semiconductor material, often silicon, and used in amplification or switching circuits. BJTs are called "bipolar" since their operation depends on both electrons and holes (charge carriers). BJTs have a "junction" because they are formed of two (usually) semiconductor regions of different properties, the boundary of which is the "junction". The three terminals of a BJT are known as the collector, emitter, and base. The BJT functions because charge carriers move from a region where they are majority carriers into a region where they are the minority carrier. Within the base, these minority carriers diffuse toward the collector, where they escape. The ability of the carriers to enter and exit the base is determined by the electric field established by a small current flowing from the base to the emitter. There are two primary types of BJTs, depending on whether the minority carriers of the base are electrons or holes: NPN or PNP.

An N region of semiconductor is doped with an extra electron, hence electrons are the majority carriers. A P region is doped with an extra hole (i.e. it is missing an electron for each atom), so holes are the majority carriers. For an npn transistor, the voltage at the collector VC must be greater than the voltage at the emitter VE by a few tenths of a volt; otherwise, current will not flow through the collector-emitter junction, no matter what the applied voltage at the base.  For pnp transistors, the emitter voltage must be greater than the collector voltage by a similar amount. For the npn  transistor, there is a voltage drop from the base to the emitter of 0.6 V.  For a pnp transistor, there is also a 0.6 V rise from the base to the emitter. In terms of operation, this means that the base voltage VB of an npn transistor must be at least 0.6 V greater that the emitter voltage VE; otherwise, the transistor will not pass emitter-to-collector current.  For a pnp transistor, VB must be at least 0.6 V less than VE; otherwise, it will not pass collector-to-emitter current. Once the transistors "turn on" the current rises linearly with base voltage in what is known as the "active region." However, the current quickly saturates and bends into a nearly horizontal line in what is known as the "saturation region". The final saturation current is dependant on the voltage from collector to emitter.

The fundamental equations describing the BJT are:
IE = IC + IB
IE = (β + 1)IB ≈ β*IB, where β is the amplification factor of the transistor.